Nr. 50 - HAMILTONIAN 3x3 2018, MAT

20 x 20 x 20 cm: wood

The object represents in an abstract form a serpent that has visited only once each of the 3 x 3 x 3 = 27 dots of an imaginary 3-D matrix, and that eventually came to rest covering all of them. In no way the serpent can bite in its own tail and create a closed loop (*).  

The serpent, has a length of 212 cm and is 4 cm thick, is able to fold herself into a cube with a side of 20 cm. 

There are many ways for the serpent to visit all 27 points: e.g. the serpent can start at any point of the matrix and go left or right, or up or down, etc.

The only way to know how many possibilities there are is by trying them one by one. The result is that here are 103346 possibilities. 

Mathematicians study the many possibilities of folding because there is a link with proteins in living material. Proteins are initially long chains of amino acid molecules that fold into a specific compact structure, which eventually determines the unique role of the protein (see Cat. Nr. 51).

(*) It can be proven that in an N x N x N matrix, in which N is an uneven number, the snake will never be able to bite in its tail. That is only possible when N is even (like e.g. in Cat. Nr. 51)